Read https://www.youtube.com/html5. Notice how it says only supported videos will be played in HTML5. However, some videos just require Adobe Flash Player. One thing you could try is clicking "Request the HTML5 player" if it is displayed on that page, then try again. If it still doesn't work or you don't see that button, you need Adobe Flash Player.

There are some videos that stopped playing properly a few days ago yet if you hover over the loading bar it will show a screenshot of the video so the video is there but it winds up saying "There was an error with this video".